/MAT/LAW117

Block Format Keyword This law represents the constitutive relation of ductile adhesive materials in 2 modes for normal and tangential directions. This law models the elastic and failure response of the material.

This material is only compatible with solid hexahedron elements (/BRICK) and the TYPE43 property (cohesive solid). This material is not compatible with any failure model. All damage and failure are defined inside of the material directly.


Figure 1. Representative scheme of the mixed mode model

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW117/mat_ID/unit_ID
mat_title
ρi                
EN ET Imass Idel Irupt      
Fct_TN Fct_TT TN TT Fscale_x  
GIC GIIC EXP_B EXP_BK Gamma

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID (Optional) Unit Identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

ρi Initial density.

(Real)

[kgm3]
EN Stiffness normal to the plane of the cohesive element.

(Real)

[Pam] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadaWcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
ET Stiffness in the plane of the cohesive element.

(Real)

[Pam] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadaWcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
Imass Mass calculation flag.
= 1 (Default)
Element mass is calculated using density and mean area.
= 2
Element mass is calculated using density and volume.

(Integer)

 
Idel Failure flag indicating the number of integration points to delete the element (between 1 and 4).

Default = 1 (Integer)

 
Irupt Mixed mode displacement law flag.
= 1 (Default)
Power law
= 2
Benzeggage-Kenane

(Real)

 
Fct_TN Function identifier of the peak traction in normal direction versus element mesh size.

(Integer)

 
Fct_TT Function identifier of the peak traction in tangential direction versus element mesh size.

(Integer)

 
TN Peak traction in normal direction (default = 0)

or, Fct_TN ordinate scale factor (default = 1)

(Real)

[Pa]
TT Peak traction in tangential direction (default = 0)

or, Fct_TT ordinate scale factor (default = 1)

(Real)

[Pa]
Fscale_x Fct_TN and Fct_TT abscissa scale factor.

Default = 1 (Real)

[m]
GIC Energy release rate for mode I.

(Real)

[Pa.m] MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbmaadmaabaGaciiuaiaacggacaGGUaGaamyBaaGaay5waiaaw2faaaaa@3BD0@
GIIC Energy release rate for mode II.

(Real)

[Pa.m] MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbmaadmaabaGaciiuaiaacggacaGGUaGaamyBaaGaay5waiaaw2faaaaa@3BD0@
EXP_B Power law exponent for the mixed mode.

Default = 2 (Real)

EXP_BK Benzeggage-Kenane exponent for the mixed mode.

(Real)

Gamma Gamma exponent for Benzeggage-Kenane law.

Default = 1 (Real)

Example (Connect Material)

Comments

  1. Mode I refers to the normal direction and mode II refers to the shear direction. δI MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaSbaaSqaaiaadMeaaeqaaaaa@3895@ is the separation in normal direction equal to δzz MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaSbaaSqaaiaadQhacaWG6baabeaaaaa@39C6@ direction. δII MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaSbaaSqaaiaadMeacaWGjbaabeaaaaa@3964@ is equal to the separation in tangential direction δII=δyz+δzx MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaSbaaSqaaiaadMeacaWGjbaabeaakiabg2da9maakaaabaGaeqiTdq2aaSbaaSqaaiaadMhacaWG6baabeaakiabgUcaRiabes7aKnaaBaaaleaacaWG6bGaamiEaaqabaaabeaaaaa@430B@ . The mixed mode displacement is referred to by δm MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaSbaaSqaaiaad2gaaeqaaaaa@38BA@ .
  2. The damage initiation displacement in mode I and mode II are respectively, δI0=TNEN MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0baaSqaaiaadMeaaeaacaaIWaaaaOGaeyypa0ZaaSaaaeaacaWGubWaaSbaaSqaaiaad6eaaeqaaaGcbaGaamyraiaad6eaaaaaaa@3DF0@ and δII0=TTET MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0baaSqaaiaadMeacaWGjbaabaGaaGimaaaakiabg2da9maalaaabaGaamivamaaBaaaleaacaWGubaabeaaaOqaaiaadweacaWGubaaaaaa@3ECA@ and for the mixed mode:(1)
    δm0=δI0δII01+β2(δII0)2+(βδI0)2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0baaSqaaiaad2gaaeaacaaIWaaaaOGaeyypa0JaeqiTdq2aa0baaSqaaiaadMeaaeaacaaIWaaaaOGaeyyXICTaeqiTdq2aa0baaSqaaiaadMeacaWGjbaabaGaaGimaaaakiabgwSixpaakaaabaWaaSaaaeaacaaIXaGaey4kaSIaeqOSdi2aaWbaaSqabeaacaaIYaaaaaGcbaWaaeWaaeaacqaH0oazdaqhaaWcbaGaamysaiaadMeaaeaacaaIWaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOGaey4kaSYaaeWaaeaacqaHYoGycqGHflY1cqaH0oazdaqhaaWcbaGaamysaaqaaiaaicdaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaaqabaaaaa@5C50@

    With the mode mix β=δIIδI MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdiMaeyypa0ZaaSaaaeaacqaH0oazdaWgaaWcbaGaamysaiaadMeaaeqaaaGcbaGaeqiTdq2aaSbaaSqaaiaadMeaaeqaaaaaaaa@3EC4@ .

  3. The maximum displacement at failure δmF MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0baaSqaaiaad2gaaeaacaWGgbaaaaaa@3985@ can be calculated using either a Power law for Irupt=1:(2)
    δmF=21+β2δm0ENGICEXP_B+βETGIICEXP_B1EXP_B MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@69FB@
    or, a Benzeggage-Kenane law for Irupt =2:(3)
    δmF=2δm011+β2ENγ+β21+β2ETγ1γGIC+GIICGICβ2ETEN+β2ETEXP_BK MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@812A@
  4. GIC and GIIC are the energy release rates between the peak traction and the maximum displacement for mode I and mode II, respectively.

    GIC=TNδIF2 MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaadMeacaWGdbGaeyypa0ZaaSaaaeaacaWGubGaamOtaiabgwSixlabes7aKnaaDaaaleaacaWGjbaabaGaamOraaaaaOqaaiaaikdaaaaaaa@4196@ and GIIC=TTδIIF2 MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaadMeacaWGjbGaam4qaiabg2da9maalaaabaGaamivaiaadsfacqGHflY1cqaH0oazdaqhaaWcbaGaamysaiaadMeaaeaacaWGgbaaaaGcbaGaaGOmaaaaaaa@4338@